Transit of sun through the seasonal nakṣatra cycle in the Vṛddha-Gārgīya Jyotiṣa¶

Indian Journal of History of Science, 56.3(2021)¶

Supplementary Material¶

Fig 1 - Yearly variation of the nakṣatra location error Ey in the seasonal solar zodiac of VGJ.¶

  • The green curves (....83 stars; ___ 27 proxy stars; -.-.-. 9 seasonal nakṣatra) refer to the Ādityacāra data of the 11th Section of VGJ.
  • The 83 constituent and the 27 proxy stars are as per Table 1.
  • Errors for the nine seasonal nakṣatra boundaries remain zero during 1210-1150 BCE.
  • The red curves refer to the twelve month solar nakṣatra data available in the 59th Section titled Ṛtusvabhāva.

Fig. 2. Error sensitivity for possible identification of Vedic star śraviṣṭhā as β Aquari and śravaṇa as β Delphini.¶

  • The readjusted 27 proxy stars and the yogatāras of Abhyankar lead to almost the same result of c 1250 BCE for the error minimum.
  • Errors for the nine seasonal nakṣatra boundaries remain zero during 1700–1350 BCE.

Fig.3. Twelve month (madhu-tapasya) or (caitra-phālguna) sun’s transit in 500 BCE as per the Ṛtusvabhāva (59th aṅga) of VGJ.¶

  • The points are joined smoothly for better visualization with markings for the seasons and the months.
  • It can be verified that all the twelve nakṣatra named in the VGJ text would have been visible sometime in the specified months.

One Year full moon overlaid on Seasons and Nakṣatras for -1500¶

One Year full moon overlaid on Seasons and Nakṣatras for -1500¶

  • Plot of RA and Dec and Full Moon size indicated

One Month moon overlaid on Seasons and Nakṣatras for -1500¶

  • Plot of RA and Dec ; Black is krishna paksha, Blue is shukla paksha
  • Size indicates the phase of the moon
<AxesSubplot:title={'center':'Moon Path - two nakshatra cycles - at -500\n Blue is shukla paksha and black krishna'}>

Plot of Nakṣatra locations in their respective divisions¶

  • Red Band indicates where the nakṣatra bound is highest

Seasons per Ādityacāra¶

  श्रविष्ठादीनि चत्वारि पौष्णार्धञ्च दिवाकरः । वर्धयन् सरसस्तिक्तं मासौ तपति शैशिरे ॥   
  रोहिण्यन्तानि विचरन् पौष्णार्धाद्याच्च भानुमान् । मासौ तपति वासन्तौ कषायं वर्धयन् रसम् ॥          
  सार्पार्धान्तानि विचरन् सौम्याद्यानि तु भानुमान् । ग्रैष्मिकौ तपते मासौ कटुकं वर्धयन् रसम् ॥   
  सावित्रान्तानि विचरन् सार्पार्धाद्यानि भास्करः । वार्षिकौ तपते मासौ रसमम्लं विवर्धयन् ॥    
  चित्रादीन्यथ चत्वारि ज्येष्ठार्धञ्च दिवाकरः । शारदौ लवणाख्यं च तपत्याप्याययन् रसम् ॥                   
  ज्येष्ठार्धादीनि चत्वारि वैष्णवान्तानि भास्करः । हेमन्ते तपते मासौ मधुरं वर्धयन् रसम् ॥ 
  (Ādityacāra; v. 47, 48, 52, 53, 54, 55)

Video of the seasonal nakṣatra boundaries over epochs¶

Table 1. Nakṣatra Constituents and proxy stars of the 11th Section of VGJ.¶

nid nakshatra rep_star vis_start_epoch vis_end_epoch left_bound right_bound num_stars_in_naks stars_in_naks daivata
#
1 N01-Ash Aśvayuk β Ari -2100 -1200 350.00 336.67 3 α Ari;β Ari;γ Ari Aśvini
2 N02-Bha Bharaṇī * 41 Ari -2200 -1250 3.33 350.00 3 * 35 Ari;* 39 Ari;* 41 Ari Yama
3 N03-Kri Kṛttikā η Tau -2050 -1150 16.67 3.33 6 * 17 Tau;* 19 Tau;* 20 Tau;* 23 Tau;* 27 Tau;η... Agni
4 N04-Roh Rohiṇī α Tau -1800 -900 30.00 16.67 5 α Tau;γ Tau;δ Tau;ε Tau;θ2 Tau Prajāpati
5 N05-Mrg Mṛgaśira λ Ori -1850 -950 43.33 30.00 3 α Ori;γ Ori;λ Ori Soma
6 N06-Ard Ārdrā γ Gem -2000 -1100 56.67 43.33 1 γ Gem Rudra
7 N07-Pun Punarvasu β Gem -2100 -1200 70.00 56.67 2 α Gem;β Gem Aditi
8 N08-Pus Puṣya δ Cnc -2200 -1300 83.33 70.00 1 δ Cnc Bṛhaspati
9 N09-Asl Āśleṣā ζ Hya -1700 -750 96.67 83.33 6 δ Hya;ε Hya;ζ Hya;η Hya;ρ Hya;σ Hya Sarpa
10 N10-Mag Maghā ζ Leo -1650 -750 110.00 96.67 6 α Leo;γ Leo;ε Leo;ζ Leo;η Leo;μ Leo Pitṛ
11 N11-PPal P Phalgunī δ Leo -1650 -750 123.33 110.00 2 δ Leo;θ Leo Bhaga
12 N12-UPal U Phalgunī β Leo -1500 -550 136.67 123.33 2 * 93 Leo;β Leo Aryaman
13 N13-Has Hasta δ Crv -2100 -1150 150.00 136.67 5 α Crv;β Crv;γ Crv;δ Crv;ε Crv Savitṛ
14 N14-Chi Citrā α Vir -1850 -950 163.33 150.00 1 α Vir Tvaṣṭṛ
15 N15-Swa Svātī α Boo -900 0 176.67 163.33 1 α Boo Vāyu
16 N16-Vis Viśākhā α2 Lib -1450 -550 190.00 176.67 2 α1 Lib;α2 Lib Indrāgnī
17 N17-Anu Anūrādhā δ Sco -1750 -850 203.33 190.00 4 β1 Sco;δ Sco;π Sco;ω1 Sco Mitra
18 N18-Jye Jyeṣṭhā ε Sco -1750 -850 216.67 203.33 3 α Sco;ε Sco;σ Sco Indra
19 N19-Mul Mūla κ Sco -1550 -650 230.00 216.67 6 ζ2 Sco;θ Sco;ι1 Sco;κ Sco;λ Sco;ν Sco Nirṛti
20 N20-PAsh P Aṣāḍhā λ Sgr -1300 -400 243.33 230.00 4 γ Sgr;δ Sgr;ε Sgr;λ Sgr Ap
21 N21-UAsh U Aṣāḍhā τ Sgr -950 -50 256.67 243.33 4 ζ Sgr;σ Sgr;τ Sgr;φ Sgr Viśvedevā
22 N22-Shr Śravaṇa α Aql -1200 -300 270.00 256.67 3 α Aql;β Aql;γ Aql Viṣṇu
23 N23-Dha Dhaniṣṭhā β Del -1300 -400 283.33 270.00 4 α Del;β Del;γ2 Del;δ Del Vasu
24 N24-Sha Śatabhiṣak λ Aqr -2200 -1250 296.67 283.33 1 λ Aqr Varuṇa
25 N25-PBha P Proṣṭapada α Peg -2100 -1150 310.00 296.67 2 α Peg;β Peg Aja
26 N26-UBha U Proṣṭapada λ Peg -1100 -150 323.33 310.00 2 γ Peg;λ Peg Ahirbudhnya
27 N27-Rev Revatī ε Psc -1900 -950 336.67 323.33 1 ε Psc Pūṣan

Path of Mars without and with Vakra¶

This chart that shows

  • Mars path from Jyeshta(1) to Jyeshta(2) to Jyestha(3) .
  • Epoch is around -590
  • Mars takes ~540 days from Jyeshta(1) to Jyeshta(2) ( no Vakra)
  • Mars takes ~720 days from Jyeshta(2) to Jyeshta(3) ( Vakra)
  • The mars path is color coded - blue visible, red not visible

Plot of Sun-Gruha angular gap annotated with visibility and rise/set events¶

Writing to file ../datasets/mercury-events.tsv
Writing to file ../datasets/venus-events.tsv
Writing to file ../datasets/mars-events.tsv

Venus morning/evening first/last visibility¶